Partial energies monotonicity and holomorphicity of Hermitian pluriharmonic maps

Abstract

In this paper, we introduce the notion of Hermitian pluriharmonic maps from Hermitian manifold into Kahler manifold. Assuming the domain manifolds possess some special exhaustion functions and the vecotor field V = JMδJM satisfies some decay conditions, we use stress-energy tensors to establish some monotonicity formulas of partial energies of Hermitian pluriharmonic maps. These monotonicity inequalities enable us to derive some holomorphicity for these Hermitian pluriharmonic maps.